It was Glen Grunwald who brought up the name before it could even be tossed at him.

“There were a lot of coaches, if we’d opened up this search, we would have reached out to,” the Knicks general manager said last night. “Namely, Phil Jackson.”

If there was a pause after the name, it was probably only one of perception or expectation. Because Grunwald immediately added, “We felt Woody was our guy.”

Woody is their guy, and you can interpret that any way you want because it applies any way you want. Mike Woodson, no longer interim coach, is Grunwald’s guy, a relationship that goes back to Bloomington, Ind., and the Indiana Hoosiers of Bob Knight. He is the franchise’s guy — a man who denied he threw his longtime agent under the tracks at Penn Station in order to get the Knicks coaching job, yet did cut loose that agent, who also happens to be a longtime stone in the shoe of the men who own and operate the Knicks.

Mostly, Woodson is a players’ guy. He is Carmelo Anthony’s guy and Amar’e Stoudemire’s guy, he is Tyson Chandler’s guy, is almost certain to be Jeremy Lin’s guy since Grunwald admitted he foresaw no course in which the Knicks would allow themselves to lose Lin in free agency.

Anthony was the one who absorbed all the slings and arrows in the immediate aftermath of the March coup that cost Mike D’Antoni his job and nudged Woodson a couple of feet to the left on the Knicks bench, but this was a team mutiny, one that can best be illustrated by the indifference they exhibited in the 42 games under D’Antoni and the ferocity they more often displayed in 24 games, and 18 wins, under Woodson.

In the end, there are probably a dozen reasons why the Knicks didn’t even bother to call Jackson officially, ranging from Woodson’s far-more-agreeable price tag to his far-more-amenable personality to the fact Anthony and Stoudemire are probably past the stages of their careers at which they would humbly agree to have a coach — even that coach — completely rearrange the furniture of their careers.

There’s the small possibility — or probability — Jackson may have wanted nothing to do with altering either his legacy or his fond Knicks memories by assuming his mentor’s chair without anything near the talent Red Holzman had all those years ago that stamped his legend.

Here’s something:

There’s no guarantee this was the wrong decision. Woodson does come with a track record. You can dismiss all you like the way his Hawks teams finished seasons, but he has now coached for parts of seven years, and every year his winning percentage has improved — .159 to .317 to .388 to .451 to .580 to .646 to .750. Yes, it will be hard to keep that going, to take the next logical step next year, from .750 to .756 (the Knicks would need to win 62 games), but Woodson does know how to win. The Knicks did respond to him. And if you watched Woodson’s old team in Atlanta melt down and downright quit in key spots in the playoffs, it’s hard to think he was the one holding them down.

Still, this becomes a whole different job for Woodson now. People watch every play, every time-out, every move a Knicks coach makes around here. And he is the incumbent now; without saying it in so many words, his campaign for the job conveniently deleted the fact he was sitting right next to D’Antoni during the worst of Knicks times this year.

No more of that. Woodson understands as much.

“This summer is pivotal for our team and our players going forward,” Woodson said. “Camp will be important. It’ll be nice to settle in and have a better camp where everyone comes back and has an opportunity to work and I can put a system in and help us win. I know expectations are very high and that’s the way it should be.”

And if Woodson doesn’t deliver to those expectations, it won’t be D’Antoni people will be comparing him to all of a sudden, but a certain other coach whom the Knicks would have reached out to if they had opened up the search.